I use two different finishes on my instruments.
French polish is, strictly speaking, an application technique rather than a finish material. It is nearly always associated with shellac, a resin excreted by the lac beetle. The shellac resin is dissolved in alcohol and then applied by hand with a rubber. It gives a beautiful finish that is like a lens in front of the wood, enhancing the colour and grain patterns with absolute clarity. It is a very thin finish and thus does not smother the sound in any way but allows the instrument to really breathe. It is not the most durable of finishes but it ages gracefully and is easy to repair. It is labour intensive and consequently a French polished guitar costs more than one with an oil finish. French polish finishes are organic and contain no nasty chemicals.
I generally use Osmo oil for oil finishing guitars. It is designed as a finish for wooden floors and is consequently quite tough. What I really like about it as a guitar finish is its tactile nature. When holding a guitar finished in Osmo oil it feels like you are really connecting with the wood. Osmo say "The foundation of Osmo wood finishes has been based upon purified and refined natural resources which are carefully harvested natural oils and hard waxes." In other words it does not contain chemicals that are harmful to the natural world or the user. A guitar finished in Osmo oil has a nice open woody sound.